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Is this correct. Intensity and sound level.

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data
    A certain sound wave has a measured intensity of 40 decibels at a distance of 125 m from the point source where the waves originated. At what distance from the source would the intensity be increased to 70 decibels.



    2. Relevant equations
    Sound Level (B) = 10 decibels log ( I/ Io)

    I = Ps / 4 pi (r^2)


    3. The attempt at a solution

    40/ 10 = log (I/Io)

    10^4 = I / Io

    10 ^4 (Io) = I
    10 ^4 (Io) = Ps / 4 pi (r^2)

    Ps = 10 ^4 (Io) 4 pi (r^2)

    so we then we find the new radius

    70/10 = log (I/Io)

    10^ 7 ( Io) = I

    10^ 7 ( Io) = Ps / 4 pi (r^2)

    solve for r 2

    r2 = √ (Ps / 4 pi (10^7) I o)

    r2 = √ (10 ^4 (Io) 4 pi (r^2) ) / (4 pi (10^7) I o)

    = 3.9 m


    Shouldn't the radius increase by much more. Because 70 Decibels is much louder than 40 Decibels.
    I'd figure that it would be by 50 meters or something.
     
  2. jcsd
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